Doors – My front door frame doesn’t support installing a storm door

I agree with Jeff Widmer -- you don't need a bigger/stronger bracket, as it's not the bracket that failed, but longer screws to properly fasten the bracket.

Given that, your jamb repair doesn't need to be structural so don't sweat how strong it is and just make it look nice with whatever product you've used before and liked. After you drill your pilot holes for the new bracket screws, drill out the repaired jamb with a bit that's larger than the screw threads so the screws don't stress your repair. Of course you want this larger hole to only be the depth of the jamb, maybe 3/4".

I am going to make the assumption that this condition has developed over time, rather than been this way since built. I am also assuming you meant an interior door, not an exterior door, since it is to a laundry area, not an entry door.

The easy answer would be to trim the door to fit better. But before we go that route, let's try to determine why the door has sagged. Open the door half way, stand in front of the handle edge, grab the knobs on both sides and try to lift the door. Is there any give? If you are able to lift the door, which would effectively close the gap you described in your question, then we have a hinge or frame issue. If you are able to lift the door to a point where the door would close properly and notice any give to the frame, here is a fix. Remove the center screw from the jam side of the top hinge. Use a 3 to 4 inch screw of similar finish to replace the one removed. This screw should reach the jack stud and can be used to move the top of the door frame closer to the jack stud, evening out the gap on the top of the door. Adjust this screw until you get the proper fit.

If the above mentioned technique doesn't work in your case, then trimming the door may be necessary. If so, carefully measure how much needs to be trimmed off, scribe a straight line on both sides of the door. Remove the door, secure it on it's side (just so it is easier to reach and work on,) and use a belt sander, plane, or DA sander to remove material just up to the scribed line. This will give you a nice straight edge. Re-hang your door and enjoy!